SPECTRA

We know what the stars are made of, know of their structures
and their lives, only because we are able to observe and analyze
their spectra. Unbroken starlight allows us to admire a star's
external characteristics; its spectrum allows us to look into its
very soul.

This site, closely coupled to The
Natures of the Stars and The Hertzsprung-
Russell (HR) Diagram, provides an introduction to the spectra
of stars and allied celestial objects. Here we examine the
principal way in which astronomers have learned so much about the
stars. "Spectra" is embedded with links that will take you back
to the appropriate parts of the above two sites.

Pass sunlight through a triangular prism or bounce it off the
finely grooved surface of a compact audio disk and see it break
merrily into a band of pure sparkling color, its "spectrum,"
familiar in the colors of a rainbow, in light glittering from
newly fallen snow, in the rings and haloes around a partly-
clouded Sun and Moon, in the flash of a
cut diamond, and in so many other facets of nature. The classic
colors red, orange, yellow, green, blue, and violet connect in a
seemingly infinite number of shades, one blending smoothly into
the next. Together they constitute the "visual spectrum" (or
"optical spectrum") because it is the part of the full spectrum
that is seen with the human eye.

The rainbow is a natural spectrum
caused by the refraction and reflection of sunlight through
raindrops, and shows that sunlight consists of a continuous run -
- a continuum -- of colors from red to violet. Note the fainter
outer bow caused by double reflections inside the raindrops.
Photo by J. B. Kaler

Stand outdoors to see and feel the radiation pouring from the
Sun. Most of the energy of the Universe is transported in this
way, by radiation. The visual spectrum of light, however, is but
a tiny portion of the whole picture, of a huge spectrum of
radiation that extends in both directions from the edges of the
rainbow. If with superhuman eyes you could see beyond red, you
would encounter the "infrared" -- felt as heat on the skin --
which would merge gradually into the familiar "radio" portion of
the spectrum. Shorter than violet you would see the ultraviolet,
that which gives us tans and sunburns, and then you would
encounter much more dangerous X-ray radiation and finally deadly
gamma rays.

The electromagnetic spectrum runs from
short gamma rays at left to long radio waves at right. The
narrow visual band, broken into its major colors, is in the
middle. From "Astronomy! A Brief Edition," J. B. Kaler, Addison-
Wesley, 1997.

Except for the energy they carry, all portions of the spectrum --
ordinary light, infrared, radio, ultraviolet -- are fundamentally
the same. They are unified by thinking of them as
"electromagnetic waves," waves of alternating strength in
electric and magnetic fields that all move through space at the
"speed of light" (called "c") of 300,000 kilometers per second
(186,000 miles per second), eight times around the Earth in the
tick of a clock. The differing kinds of radiation simply have
different wavelengths, that is, the separations between crests in
two successive waves. Visual radiation is in the middle, with
wavelengths that extend from 0.00004 centimeters for violet light
to about 0.00007 centimeters for extreme red. These wavelengths
are so short that astronomers use a small unit of distance, the
"Angstrom" (A), which is 0.00000001 centimeters long. The violet
limit therefore falls at 4000 A and the red limit near 7000 A or
a bit longer. Infrared runs from the red limit to about 0.1
millimeter, and the radio to as long as you wish, even to
kilometers. Ultraviolet runs from 4000 A down to about 100 A, X-
rays take over to about 1 A, and these are followed by the gamma
rays to no known lower limit. The named divisions are artificial
and serve only to block out large spectral segments.

Though light and its partners can act like waves, at the same
time they can act like a stream of particles. In a crude sense,
these particles, called "photons," carry the waves. The smaller
the wavelength of the photon the more energy it carries, that is,
the greater the ability of the photon to act on some physical
substance. Long radio waves are generally benign. You can live
near a high-powered radio transmitter with no effect on you and
are quite unaware of all the radio photons that constantly
surround and pass through you. Shorter-wave photons have
increasingly potent effects. Infrared is felt as heat, visual
radiation excites the chemistry of the eye, ultraviolet burns,
and no one wants to stand in front of an active X-ray machine for
long. A single gamma ray photon can carry the energy of over a
million million million radio photons.

Light and its partners can be manipulated in a variety of ways.
The most familiar is "reflection," in which light is bounced from
a surface, the light coming off at the same angle at which it
hits, resulting in your undistorted face looking back at you from
a mirror. Radiation travels at "c" only in a vacuum. When it
passes into a substance, it slows and can be bent, a common
phenomenon called "refraction." The effect is easily seen when
looking at something through water. Refraction by a curved lens
focuses radiation to create an image. Turned to the sky and
attached to a detector, the lens becomes an astronomical
telescope. (A curved mirror can create a similar image by
reflection.) The speed of an electromagnetic wave in a medium
depends on its wavelength. Violet light is slowed in a glass of
water significantly more than red light. As a result shorter
visual waves refract more than do longer ones. Refracted light
is therefore "dispersed" or spread out into its spectrum,
creating a rainbow -- or the spectrum of a star. Spectra can
also be created by the interference of light waves, the
phenomenon that makes the brightly colored patterns seen
reflected from a compact audio disc and the halos often observed
next to a bright, partly clouded Moon.

Astronomers produce spectra by means of a "spectrograph" affixed
to the telescope. The oldest form of the device was visual (a
spectroSCOPE), and consisted of little more than a prism in a
tube fixed to the end of the telescope, the refracted light
focused by an observer's eyepiece. By the turn of the 20th
century, spectra were being recorded photographically. In the
middle of the century, prisms were replaced by "diffraction
gratings," finely ruled surfaces that produce spectra by the
interference of light waves. In the modern spectrograph, light
is sent from the telescope onto a "collimator," a curved mirror
that straightens the converging beam. The collimator sends the
beam to a reflecting grating that makes a spectrum, the colored
light then focused by a camera onto a detector, usually a
"charge-coupled device," or "CCD," that records the spectra
digitally. Spectra are commonly seen reproduced either
photographically or graphically.

The spectrograph, fitted to the base of
the telescope (seen at the top), breaks light into its component
colors and records the spectrum. Light from a star goes straight
to the collimator at the bottom of the instrument and is
reflected back up to a diffraction grating in the middle. It is
then reflected down and to the left to a digital detector for
storage and display on a video terminal. University of Arizona
Steward Observatory spectrograph photo by J. B. Kaler

Electromagnetic energy cannot be separated from matter. Indeed,
matter both creates and destroys radiation. All the matter
around us is made ultimately of tiny particles, of "atoms" of
different kinds. These in turn are made of yet-smaller
particles. The atom, in a conceptual sense, can be thought of as
consisting of a nucleus made of one or more protons (particles
that carry positive electric charges) and neutrons (neutral
particles with masses about equal to those of protons). The kind
of atom -- or "chemical element" -- whether hydrogen, oxygen, or
iron, depends only upon the number of protons in the nucleus (for
these, 1, 8, and 26 respectively). The nucleus is surrounded by
a cloud of much lighter electrons that carry negative electric
charges exactly equal in amount to those carried by the protons.
The electrons are bound to the nucleus by the "electromagnetic
force," the force responsible for the production of
electromagnetic radiation. The protons are bound together even
though of the same charge by the much more powerful short-range
"strong force," which is carried by both protons and neutrons,
but not by the electrons. The neutrons' job is to add strong
force to help keep the nucleus together.

A normal atom, with equal numbers of protons and electrons, is
electrically neutral. You get no electric shock by touching
matter in its normal state. It is easy, however, to remove
electrons from an atom and to electrically unbalance it. The
result of electron removal is a positively charged "ion." In
fact, all the electrons can be removed to reveal a bare nucleus.
Hydrogen, with one electron and one proton, has but one
ionization "state" (the lone proton). Iron, with 26 electrons
has 26 ionization states, each more positively charged than the
next as more and more electrons are taken away.

The electrons of two or more atoms can link together to form
chemical bonds that make molecules from the chemical elements.
The atoms can be the same or can be different. Common examples
of such "chemical compounds" are molecular oxygen (two oxygen
atoms locked together), water (two hydrogen atoms coupled with an
oxygen atom), and carbon dioxide (two oxygens and a carbon). The
molecules have characteristics that are completely different from
their component atoms. There is no limit on the number of atoms
that can be linked, and as a result there is an infinite number
of kinds of molecules, the collection of which gives us all the
riches of the natural world, including life.

The number of neutrons present in any kind of atomic nucleus is
not fixed. All atoms have a set of variants called "isotopes" in
which the proton number is the same but the neutron number is
different. For example, the most common kind of hydrogen has
only one proton. But you can attach a neutron to the proton and
still have hydrogen. This heavy form, called "deuterium," is
present in nature. About 0.001% of all the water you drink is
deuterium oxide instead of normal water, but since the different
isotopes of an atom have about the same chemical properties,
deuterium has no special effect on you. The great bulk of iron
(92%) has 30 neutrons coupled to its 26 protons, but 6% has 28
neutrons, 2% has 31 and a small remainder 32 neutrons. Some
elements, like beryllium and scandium, have but one stable (see
below) isotope. Tin, with 10, holds the record number.

For any atom there is a limit to the number of neutrons allowed,
that is, on the number of different stable isotopes. If there
are too many or too few neutrons, the nucleus becomes UNstable
and falls apart with the emission of particles (neutrons, helium
nuclei, electrons) and high-energy electromagnetic radiation
(notably gamma rays). Such "radioactive" isotopes can be quite
dangerous. A radioactive isotope decays away at a steady rate
defined by its "half-life," the time it takes half of the
substance to turn into a lighter product. The shorter the half-
life, the more dangerous the isotope. Some radioactive isotopes
last for billions of years, others for fractions of a second.
Some chemical elements have no stable isotopes at all and are
therefore rare. All elements heavier than bismuth (83 protons)
are radioactive, the set including familiar radium and uranium.
Uranium (92 protons) has a very long half life, and as it decays
to lead, it produces the Earth's radium (88) along the way. Most
of the helium on Earth is a by-product of such decay. Since the
decay rates of different radioactive elements are known from the
laboratory, the ratio of the abundance of the parent element
(uranium for example) to the daughter product (for uranium, a
specific isotope of lead) in a rock gives the rock's age, the
time since it solidified. We can therefore date the birth of the
Solar System and the Sun to 4.5 billion years ago from the ages
of the oldest rocks (meteorites and rocks from the Moon).

Normal non-radioactive matter can radiate too, not by nuclear
decay, but as a result of the heat it contains. The kind of
radiation emitted depends on temperature. If you turn on your
toaster in the dark, you can see it glow, the visual spectrum
radiated by the hot metal. The hotter the toaster's radiating
element, the higher the energy of the radiation it can emit. At
low temperatures you see only red, but if you could increase the
temperature high enough, the toaster would emit blue and then
violet light as well as red. At a million degrees Kelvin
(centigrade degrees above absolute zero, -273 degrees C) it would
even emit gamma rays (and really burn the toast). At very low
temperatures it will still radiate. At a few hundred degrees,
the temperature of the kitchen, it radiates infrared. Even in
the cold of interstellar space, the toaster would produce radio
photons (space toast?). As a general rule, as temperature goes
up, a body produces ever more radiation at all wavelengths
shortward of a limit that pushes ever further toward shorter
wavelengths. (A cold body radiates radio, a warmer one infrared
and radio, warmer yet visual, infrared, and radio, and so on, all
kinds present increasing in amount with increasing temperature.)
A gas under high pressure will radiate as well as a hot solid.
Star colors thus reflect
temperature, reddish stars cool (3000 to 4000 degrees Kelvin),
bluish ones hot (over 20,000 degrees Kelvin). As a result, we
can determine the temperature of a star from its color, more
specifically from the details about how the radiation is
distributed throughout its spectrum.

Now go to the heart of the matter, to how free-flying radiation
interacts with atoms to give us detailed information about stars
and other celestial bodies. Send radiation from a hot,
incandescent solid through a gas of low density and watch what
happens. The electrons that surround an atom have a minimum
energy below which they cannot go (a discovery of "quantum
mechanics" made in the early part of the 20th century). The
electrons will naturally seek this lowest energy level.
If you move the electrons outward, away from the nucleus, you
give them more energy. However, electrons are very specific
about what energies they will take. For any given atom or ion,
only certain specific electron energies, that is, specific
energy levels, are allowed. Electrons can be moved from
one energy level to another by collisions among atoms or by
absorption of photons. However, an electron in a specific level
cannot absorb part of a photon, but must absorb all or none of
it. As a result, only photons with particular energies, those
that correspond to differences between the various energy levels,
can be absorbed from the flow of passing radiation. Since photon
energy corresponds to wavelength, only specific wavelengths (or
colors) can be absorbed. And since the electron structures are
different for each kind of atom or ion, the photon energies that
each kind will absorb are also different. When we look at the
spectrum from the hot source after it has gone through the low-
density gas, we therefore see narrow gaps at particular
wavelengths where the light is diminished or even gone
altogether. Because of the way they appear, these gaps are
called "absorption lines." Each atom or ion has a unique set of
absorption lines. Hydrogen has only four in the visual spectrum:
at wavelengths of 6563 A in the red (called H-alpha), at 4861 A
in the blue (H-beta), and at 4340 A (H-gamma) and 4101 A (H-
delta) in the violet), whereas iron has thousands.

The deeper you go into a star, the hotter and denser the gas.
The lower layers tend to radiate all the colors rather like a hot
solid, while the upper layers act something like the low density
gas of the last paragraph through which the radiation passes.
Stars are made of the same stuff as found in the Earth (though
not in the same proportions), and contain all of nature's
chemical elements. As a result, the spectrum of a star displays
an extraordinary mixture of absorption lines. Over 100,000
absorption lines are visible in the Sun's spectrum.

The solar spectrum is filled with
absorption lines at particular colors or wavelengths, each dark
line associated with a particular atom or ion. The pair in the
orange, for example, are made by neutral sodium, the trio in the
yellow by magnesium. Kitt Peak National Observatory.

The absorption lines in the Sun and stars can be identified with
individual chemical elements or molecular compounds by comparing
their positions in the spectrum (their wavelengths) with those
observed from pure sources in the laboratory. Some absorptions
are very weak, just shallow dips in the spectrum, whereas others
are completely black. The "strength" of an absorption line --
the amount of energy removed from the spectrum -- depends on the
amount of the particular chemical element in the star causing the
line and on the efficiency of absorption. The efficiency is
crucial. Hydrogen dominates the Sun, yet absorption lines of
ionized calcium dominate the solar spectrum even though there is
440,000 times as much hydrogen as calcium. Hydrogen has a low
efficiency of absorption, whereas that of ionized calcium is very
high. The efficiency depends on the availability of electrons to
move to higher energies and on atomic factors, namely the
likelihood of absorption in the presence of a passing photon.
The efficiencies depend critically on temperature and can be
calculated from theory or measured in the laboratory. Once they
are known, we can calculate the abundances of the atoms from the
strengths of the absorption lines and therefore calculate the
chemical composition of the outer part of a star. Relative
absorption line strengths can also be used to find temperatures
and densities.

The Sun displays an enormous number of
spectrum lines, over three dozen appearing here in a 20 A-wide
stretch in the yellow part of the spectrum. Roman numeral "I"
stands for the neutral ion of an element, "II" for the once-
ionized version. Different lines have different strengths. The
ionized iron lines are nearly black, whereas those produced by
the much rarer elements yttrium (Y), neodymium (Nd), and
lanthanum (La) are very weak. E. C. Olson, Mt. Wilson
Observatory.

What goes up must come down. Electrons, like anything else, will
attempt to seek their lowest energies. If the electrons gain
energy by the absorption of photons, or perhaps by collisions,
they must eventually lose it again. They can lose it in
collisions or they can, instead of absorbing photons, radiate
them. Since the absorption wavelengths are tightly defined, so
are the emission wavelengths. If we look at a heated low-density
gas WITHOUT looking at a bright source behind it, we will see
BRIGHT lines of color at the same spectral wavelengths at which
we before saw dark absorptions. For any given atom or ion, the
emission spectrum is a simple reversal of the absorption
spectrum. Emission lines are easy to produce in the laboratory
simply by heating a low-density gas, allowing collisions to kick
the electrons to higher energies. The emissions are produced
when the electrons drop back down to lower energies. Emission
lines are radiated by street lamps (the orange ones radiating
sodium lines, the blue ones mercury lines), neon signs, and
fluorescent bulbs. They are also produced by clouds of
interstellar gas ( nebulae) that are
heated and ionized by nearby hot stars. Under some
circumstances, stars can radiate emission lines too. For
example, Mira variables
have hydrogen emission lines that are excited by powerful shock
waves -- sonic booms -- made by the stars' pulsations.

Hydrogen emission lines are radiated by
a hot, thin hydrogen gas, and appear at the same wavelengths as
the hydrogen absorption lines. From "Astronomy! A Brief
Edition," J. B. Kaler, Addison-Wesley, 1997.

Emission nebulae, clouds of interstellar gas that produce
emission lines, exist in three main forms: as diffuse nebulae
(like the Orion Nebula below), planetary nebulae (like the Ring Nebula in Lyra, also below), and
supernova remnants. Diffuse nebulae are the leavings of star
formation, clouds of dusty interstellar gas that are ionized by
ultraviolet radiation from the massive hot stars near or within
them. Planetary nebulae are ejecta of dying stars that are lit
by even hotter, nearly-exposed stellar cores that are on their
way to becoming white
dwarfs. Supernova remnants are a combination of hot ejecta
of exploding stars (supernovae) and local
interstellar matter heated by shock waves from the
explosion.

The Orion Nebula (left), a great cloud
of interstellar gas ionized by hot young stars at its center, and
the Ring Nebula (M 57, right) both radiate emission lines,
including those of hydrogen seen above and a huge number of
others. The ionizing stars of the Orion Nebula (Theta-1 Orionis) are lost in the
nebula's bright glow, while the ionizing core of the Ring Nebula
is at the Ring's center. University of Illinois Prairie
Observatory

Nebular emission lines fall into two basic types: permitted
recombination lines and forbidden (collisional)
lines. Recombination lines are caused when atoms in a nebula are
ionized by absorbing energy from the ultraviolet light radiated
by a nearby or embedded hot star. When free electrons are re-
captured by various ions, they can land on any energy level. The
electrons then skip downward, radiating emission lines as they
go. Hydrogen and helium produce only recombination lines, as do
atoms and ions of oxygen, nitrogen, carbon, neon, and others.
Forbidden lines are not really forbidden, just difficult to
produce from energy levels that do not readily interact with each
other (making the transitions of electrons between them
difficult). They are indicated by square brackets, and are
caused when energetic free electrons collide with atoms or ions
whose electrons are in the bottom level and excite these bound
electrons to higher levels, from which they eventually drop
downward to radiate emission lines. Analysis of line strength
allows the determination of nebular temperature, density, and
chemical composition.

The planetary nebula BV-1 displays a
variety of emission lines. The producing ion is indicated by
Roman numeral, "I" for neutral, "II" for single ionization (one
electron missing), "III" for double ionization (two missing), and
so on. The full spectrum is at the bottom. The inset above it
shows a vertically expanded view. Hydrogen and helium produce
recombination lines. Square brackets indicate collisional
(forbidden) lines, which include those of nitrogen, oxygen, neon,
argon, and sulphur.

Because the efficiencies of absorption depend on temperature, so
do the appearances of the spectra of the stars. Stellar spectra
were first observed in the middle of the 19th century. To the
great confusion of the astronomers of the time, most spectra
looked nothing like the solar spectrum. Some, like that of Vega, had powerful hydrogen lines, whereas
others had none at all and displayed what were later shown to be
molecular lines of titanium oxide. It looked as though different
stars were made of different elements. As an aid to
understanding, astronomers began classifying the spectra, the
schemes culminating about 1890 in the one still used today when
E.C. Pickering lettered the stars according to the strengths of
their hydrogen lines, his assistants Annie Cannon, Antonia Maury,
and Williamina Fleming aiding in development and observation. As
observation improved, they dropped some letters, rearranged
others according to different spectral criteria, and added
decimalization. The result was the classic seven-group sequence
OBAFGKM. A bit over a century later, as a result of new
technologies, astronomers added another two classes whose spectra
contained molecules, L and T. About the first thing any
astronomer wants to know about a star is its class. The Sun is class G.

In the modern spectral sequence, OBAFGKMLT, the hydrogen
absorption lines weaken in both directions away from class A.
Various other absorptions round out the picture. It was noted
very early that the spectral sequence in this form correlates
with color, ranging from a
blue tint for O and B stars to reddish for class M. Since color
depends on surface temperature, so must the spectral class.
Stars of class T and cool L radiate only in the infrared and are
invisible to the eye. Class T contains only brown dwarfs, while class L (and
even cool M) is a mixture of brown dwarfs and true dwarfs that
run full hydrogen fusion. (The
temperatures in the table below are for main sequence dwarfs.)

The visual colors are actually subtle and as much reflect where
most of the light lies in the spectrum as the color a person
would actually view. Classes A through G all look rather white
to the eye. Decimal subdivisions of the spectral classes go
toward lower temperature, for example, A0 lies at the hot end of
class A near a temperature of 10,000 K, while A9 is at the cool
end near 7200 K. The Sun, with a temperature of 5800 K, is class
G2. The above temperatures are for main sequence dwarfs. Those
of other luminosities may differ,
especially in classes G and K, where the temperatures of giants are a up to a few
hundred degrees lower and those for supergiants are lower yet.

The classic spectral sequence is
illustrated by the spectra of real stars in a historic image
published in 1901. The strong lines in class A (here, the star
Sirius) are hydrogen. Neutral helium
appears along with hydrogen in class B (Alnilam, Epsilon
Orionis), while ionized helium is strong in class O (Naos, Zeta Puppis), the hydrogen lines
nearly gone. Hydrogen weakens downward too, toward lower
temperature, nearly disappearing by class M2 (Betelgeuse). The strong lines to the
left in classes F (Canopus), G (Capella), and K (Arcturus) are those of ionized calcium.
The other lines in these cooler classes are those of other
metals. At the bottom, in class M7 (the long-period variable star Mira), we see bands of absorption produced
by the titanium oxide molecule. Annals of the Harvard College
Observatory, vol. 23, 1901.

Analyses of the spectra show that all the stars of the main sequence, those fusing
hydrogen in their cores, have similar chemical compositions, all
about 90% hydrogen, 10% helium, and 0.1% everything else (by
number of atoms). The 0.1% remainder has a distribution among
the elements that is quite similar that found in the Earth and
Sun. The differences in stellar spectra, at least for main
sequence stars, are caused almost entirely by differences in
ionization (after all, if sodium is all ionized, the absorptions
of neutral sodium will not be present) and the by the way in
which the absorption efficiencies change with temperature.

Classifying stars is something of an art form that comes with
practice. Each spectral class is defined by the spectrum of a
standard star against which the other stars are compared. The
classifier eventually memorizes the standards and can classify
the spectrum of a random star very quickly. Annie Cannon
classified well over 300,000 stars in her lifetime, one at a
time. Modern classifiers are now heading toward automated
systems that use computers and complex software to simulate what
a human eye and mind can do.

Although temperature reigns supreme in defining the spectrum of a
star, the density of the gas in the region where the absorption
lines are formed plays a role too. Giant and supergiant stars are so
large that the densities in their outer regions are low, which
subtly changes the appearance of the stellar spectrum. For
example, the hydrogen lines are quite broad in main sequence (dwarf) stars as
a result of the disturbance of the hydrogen atoms caused by
collisions. In the huge distended supergiants, however, lower
density leads to lowered collision rates, and as a result the
hydrogen lines are narrow. In K-type giants, the dark bands of
the CN (cyanogen) molecule are stronger than they are in class K
main sequence stars. Each spectral class in fact has its own set
of criteria. As a result, once we know what these criteria are,
we can tell if a star is a giant, supergiant, or of any other
category, from its spectrum alone. Roman numerals are used to
indicate size and luminosity, "I" for supergiants, "II" for
bright giants, "III" for giants, "IV" for "subgiants" (stars that
are developing into giants), and "V" for the main sequence. The
result is the "MKK class" of the star, named after the 1940s
developers of this system, W. W. Morgan, P. C. Keenan, and E.
Kellman. Vega is an A0 V star, Polaris is F7 I or II, and Aldebaran is K5 III. The Sun is a G2 V star. White dwarfs are just
called "white dwarfs," or "D." All these classes are arrayed on
a plot of luminosity (as expressed through absolute visual magnitude)
vs. spectral class called the Hertzsprung-
Russell Diagram.

Only the main sequence runs through all the spectral classes,
OBAFGKMLT. With one known exception (the odd variable supergiant
V 838 Monocerotis) there are no giants, subgiants, or supergiants
of classes L and T, both of which contain only low mass dwarfs
and brown dwarfs that are
insufficiently massive (below 0.075 solar mass) and too cool
inside to run full hydrogen
fusion. Class L is a mixture of real dwarfs and brown
dwarfs, while class T consists entirely of brown dwarfs.

The apparent visual
magnitude of a star in the sky depends on the star's actual
luminosity and its on its distance. If we know the distance from
parallax or from some
other means, we can calculate the absolute magnitude. Such
calculations have allowed us to learn the absolute magnitudes of
all types of stars and to construct the HR
diagram. We now work backwards. From the spectrum we
determine the class of a star and thus know its absolute
magnitude. We can even discriminate within a class, for example
brighter giants as opposed to lesser ones. Comparison with the
observed apparent magnitude then yields distance. Such
"spectroscopic distances" allow us to work our way across the
Universe, as our ability to measure parallaxes are limited to
stars only within a thousand or so light years.

Main sequence stars have similar chemical compositions. But once a star
begins to die and evolve, the rules can change. Newly-minted atoms made by
nuclear reactions deep within a star can rise to the surface and change the
star's apparent chemical composition, and as a result, its spectrum. The
most famous examples are the carbon
stars, which display bands of carbon molecules. Almost all are giants. They were originally called class
"N" in the old Pickering system. N stars have roughly the same low
temperatures as the class M giants, if not a bit lower. Class R, consisting
of warmer carbon stars (more like class G and K), was added later. R and N
are now lumped together under class "C" for "carbon." Class "S" is used for
stars that have intermediate carbon abundances wherein the carbon content is
roughly equal to that of oxygen. Their spectra have strong bands of
zirconium oxide rather than the titanium oxide of oxygen-rich class M giants.
The exception to the "giant-star rule" is a rare class of main-sequence
carbon stars that have been contaminated by evolving companions.
Other variations in chemical composition can be indicated by adding a letter
to the spectral class, for example "Ba" for the strong barium lines that
denote barium stars.

The term "dwarf" is used in stellar astronomy in a variety of
ways. Main sequence stars
are commonly called "dwarfs." "White dwarfs," on the
other hand, are a sequence of dead stars that have lost their
outer envelopes and consist of little more than spent, old
nuclear-fusing cores. There is also a set of stars that are
similar to ordinary dwarfs except that compared to ordinary
dwarfs they are somewhat too dim for their temperatures (or too
hot for their luminosities, depending on how you look at them).
They are therefore called "subdwarfs." On the HR diagram they run just to the left of the
main sequence from about class G on down toward cooler stars.
Like ordinary main sequence dwarfs, subdwarfs run off the energy
generated by nuclear fusion,
specifically the fusion of hydrogen into helium. Their
distinctiveness is caused by a severe underabundance of metal
atoms. A lower metal abundance makes the gases more transparent,
which changes the stars' structures and the quality of the
radiation they emit. Typically, subdwarfs contain only about a
hundredth the iron of the Sun (relative to hydrogen), but at
their most extreme the iron abundance (along with the abundances
of other heavy elements) drops to only a ten-thousandth solar.
Subdwarfs evolve into giants
and white dwarfs just as do ordinary dwarfs.

As stars of the Galaxy age,
they dump the by-products of nuclear fusion into the interstellar
gases through their winds or
supernova explosions.
New stars are then made from gases that have been enriched in
chemical elements from prior stellar evolution. As a result,
younger stars contain more of the leavings of older stars, and
therefore contain more heavy atoms, including the metals.
Because of their low metal content, subdwarfs must be among the
oldest known stars. With a relatively high metal content, the
Sun, 4.5 billion years old, is relatively young. Most of the
stars of our Galaxy are distributed in a great disk almost
100,000 light years across. The subdwarfs and their kind are
part of a huge, rather spherical halo that encompasses the disk,
showing that the halo was the first part of the Galaxy to form.
Subdwarfs are therefore all very old. From the lifetimes of the oldest
stars, we calculate that the Galaxy dates back to about 15
billion years ago.

All stars orbit the Galaxy
on slightly (sometimes greatly) different paths, and therefore
must move relative to each
other. Could you watch a constellation
for millions of years, you would see the stars slowly changing
positions, the motions destroying the figure and helping create
new ones. Stars also move along the line of sight, some going
away from us, some coming toward us. If a star moves toward us,
its light waves seem to come more frequently and the wavelengths
seem shortened; if the star is moving away from us, we see the
reverse, the wavelengths seeming to be longer. The Doppler
effect is easily seen in water waves and heard in sound
waves, the latter affecting the pitch of a passing car or
airplane, which is higher when approaching, lower when receeding.
The degree of shift depends on the speed along the line sight
(the radial velocity) compared to the speed of the wave.
If the speed were high enough, a good fraction the speed of
light, a star would actually change color, seeming too blue if
coming at us, too red if going away. Stellar speeds, however,
are generally at most only a few tens of kilometers per second,
far less than the speed of light, so color changes are not at all
visible directly to the eye. (The exceptions are galaxies with large spectral
redshifts.) However, the
Doppler effect also causes changes in the wavelengths of spectrum lines that ARE readily detectable.
At the modern limit, astronomers can measure shifts produced by
line-of-sight motions that are as small as a few meters per
second, less than the speed of a good runner. Combining data on
velocities along the line of sight with those determined across
the line of sight (from a star's angular shift and distance)
allows us to find the star's actual speed relative to the Sun and
to construct a picture of the internal motions in the Galaxy.
Doppler shifts are also seen in nebular
spectra, where they can be used to assess both velocities and
expansion rates. They are crucial in the detections of planets, whose gravities can cause the parent
stars to move slightly back and forth along the line of sight,
from which we can derive orbtial sizes and lower limits to
planetary masses.

A great many stars are readily seen through the telescope to be
double. However, if the
stars are too close together, the observer will see them as one,
the two images forever blurred together. We can still separate
them by means of the spectrum. If the stars of a double are of
comparable brightness, the spectrum will be the composite of the
two. Unless we are looking directly down the orbital axis (the
orbit perpendicular to the line of sight), as the pair orbit each
other, the two alternately move toward and then away from the
observer. As a result, the spectrum of each star is Doppler shifted first one way and then the
other. As one spectrum is shifted to the blue (to shorter
wavelengths), the other is shifted to the red (to longer), and
vice versa. From the doubled lines that shift back and forth, we
know that there are two stars in the system. From the degree of
shift, we can derive the back-and-forth speeds of the stars.
Since the orbit is most likely tilted to the line of sight, these
observed speeds are lower limits to the true orbital velocities,
from which we can find lower limits to the stars' masses through
gravitational theory. If the star is an eclipsing double, then from
the light curve (the graph of magnitude against time) we can find
the orbit's tilt and thus derive actual masses.

If the components of a very close double star system are very
different in brightness, then only one set of absorption lines
will be seen. We will still see the one set shift back and forth
as the stars orbit, however, and can still tell that the star is
double. Such "single-line" stars (so-called because there is
only one SET of lines, that is, the observed lines are not
doubled) provide limited information on masses, but if we can
estimate the mass of the star we see from its nature and
brightness, then we can derive a lower limit to the mass of the
invisible companion.

Two stars of a very close double can
exchange matter through tides, the mass usually flowing from the
larger star to the smaller one. Such flowing gas has a low
density and radiates emission lines that
are superimposed on the spectrum of the double and give away the
fact that the stars are interacting. From the kinds and natures
of the emission lines and from their Doppler shifts we can learn the rates,
masses, and the speeds of the flows to build up a picture of how
the interactions actually take place.

The "single-line" concept has a powerful application in the
discovery of planets
orbiting other stars. In a double star system, each star
affects the other and each revolves around a common center of
mass. Each star therefore moves back and forth along the line of
sight. Even an orbiting planet will make its star shift back and
forth by a small amount. The Sun moves at a speed of about three
meters per second as a result of Jupiter's pull. The amount by
which a planet will shift a star's spectrum is easily within the
range of modern measurement. From such subtle reflexive motions,
we infer the masses of tiny bodies, of planets. Hundreds have
been found with masses that range from those of brown dwarfs down to roughly
comparable to that of Earth. Planets are also found if they
transit in front of their stars, causing dips in brightness. If
the planets are detected by both techniques, we can find
planetary masses, radii, and densities. Transits also
potentially allow the spectra of the planetary atmospheres to be
examined.

To know the stars

In examining spectra, we have moved from the very small, from
little waves and atoms, to the very large, to stars, and then
down in scale to planets. But our Sun and planetary system came
from "out there," among the stars. To know ourselves, therefore,
we must understand the stars and their natures. But the only way
of actually understanding them is to understand and appreciate
their spectra, the colored rainbows that lead us into their
depths. Without spectra, little of stellar natures would be understood and we
would still be looking at the sky in ignorance instead of with
the modern wonder of discovery.